Nearly every bot can, except RID from my understanding. In terms of which executes them most successfully, Epicbot hands down.
RiD can solve 3/18 randoms at the moment.
Simba can solve many of the randoms (more than RiD does, but idk the exact number)
RiD & Simba both log out if they get a random they cannot solve.
The injection bots can solve some of them, however there are many that are bugged out and broken, which will lead to your account being stuck in an infinite loop, constantly repeating the same action over and over again in the random, even if it's unsuccessful or wrong for that random. I've seen it happen, and I know others who it has happened to. They definitely need to improve their failsafes to log out in the event of a random it cannot successfully solve.
Also, Jagex said they are removing randoms soon, most likely after Bot Nuke (which is *rumored* to be on Oct 25th, the 1 year anniversary of the first Bot Nuke, 2 days before Bonus Exp weekend, but again, that is just a rumor) because Jagex said that after Nuke and BotWatch is fully activated, there won't be any real use for randoms since most bots can solve them, and they are known to greatly confuse many new users. Essentially no randoms soon will mean bots like RiD and Simba will be very very easily capable of running 24/7 without issues